I couldn't find an exact description in Brown's novel, but one offered by naturalist and guide to the Western States Thomas Henry offers a very concise description of Pine Ridge, which has not changed much at all since Brown wrote his novel (1970)about the plight of the Native Americans. Here is an excerpt and a link below:

At 1.7 million acres, the Pine Ridge is the second largest Indian reservation in the country. It is home to the Oglala Lakota nation, and its inhabitants usually refer to it simply as "the Rez." Ranging over the two counties of Shannon and Jackson, it lies just south of Badlands National Park and the Buffalo Gap National Grassland.

The terrain is stunning, made up of hills, cliffs, buttes, mesas, badlands and a surprising number of redcedar dotted valleys. A vast portion of it is wild prairie, which I took to be primarily the shortgrass variety, given the paucity of rain which falls here.In one of those strange contradictions so common out west, this is one of the loveliest parts of the Great Plains, but it's also one of the saddest. A few figures might give you some idea.The population of the Rez is around 30,000. Shannon is the poorest county in the nation, with an average annual family income of $3,700. Unemployment hangs around 80%, and life expectancy is 48 for men and 52 for women. About half the people over age 40 have diabetes, tuberculosis is common and the alcoholism rate is the highest in the United States. [footnote]